Hamiltonian of a flux qubit-LC oscillator circuit in the deep-strong-coupling regime.
Hamiltonian of a flux qubit-LC oscillator circuit in the deep-strong-coupling regime.
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DOI：
10.1038/s41598-022-10203-1
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发表时间：
2022-04-26
影响因子：
4.6
通讯作者：
Semba, K.
中科院分区：
文献类型：
--
作者：
Yoshihara, F.;Ashhab, S.;Fuse, T.;Bamba, M.;Semba, K.
我们推导出由电感耦合到LC振荡器的单约瑟夫森结通量量子位组成的超导电路的汉密尔顿算子，并将推导出的电路汉密尔顿算子与描述耦合到谐振子的两能级系统的量子拉比汉密尔顿算子进行比较。我们表明，有一个简单的，直观的对应关系之间的电路哈密顿量和量子拉比哈密顿。虽然存在整个谱的整体移位，但直到第七激发态的电路哈密顿量的能级结构仍然可以通过量子拉比哈密顿量很好地拟合，即使在耦合强度大于量子比特和振荡器的频率的情况下，即，当量子位振荡器电路处于深强耦合状态时。我们还表明，虽然电路的哈密顿量可以通过一个单一的变换包含一个电容耦合项的哈密顿量，得到的电路哈密顿量不能近似的量子拉比哈密顿量的变体，使用类似的程序映射到泡利和谐振子运营商的电路变量，即使是相对较弱的耦合。通量计和电荷计之间的这种差异来自量子比特哈密顿本征态的性质。
We derive the Hamiltonian of a superconducting circuit that comprises a single-Josephson-junction flux qubit inductively coupled to an LC oscillator, and we compare the derived circuit Hamiltonian with the quantum Rabi Hamiltonian, which describes a two-level system coupled to a harmonic oscillator. We show that there is a simple, intuitive correspondence between the circuit Hamiltonian and the quantum Rabi Hamiltonian. While there is an overall shift of the entire spectrum, the energy level structure of the circuit Hamiltonian up to the seventh excited states can still be fitted well by the quantum Rabi Hamiltonian even in the case where the coupling strength is larger than the frequencies of the qubit and the oscillator, i.e., when the qubit-oscillator circuit is in the deep–strong-coupling regime. We also show that although the circuit Hamiltonian can be transformed via a unitary transformation to a Hamiltonian containing a capacitive coupling term, the resulting circuit Hamiltonian cannot be approximated by the variant of the quantum Rabi Hamiltonian that is obtained using an analogous procedure for mapping the circuit variables onto Pauli and harmonic oscillator operators, even for relatively weak coupling. This difference between the flux and charge gauges follows from the properties of the qubit Hamiltonian eigenstates.
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